Decoherence of Bose-Einstein condensates in microtraps

We discuss the impact of thermally excited near fields on the coherent expansion of a condensate in a miniaturized electromagnetic trap. Monte Carlo simulations are compared with a kinetic two-component theory and indicate that atom interactions can slow down decoherence. This is explained by a simple theory in terms of the condensate dynamic structure factor.

Figure 1

Expansion of a self-interacting Schrödinger field in a noisy potential, single realization. The normalized spatial density is plotted at different times given in the inset. Parameters in Eq. (1): interaction strength $gN=10$, noise strength $\gamma =1$, correlation length $l_{\text{corr}}=0.1$. Harmonic oscillator units with respect to the initial confinement frequency $\Omega$ are used: $t\mapsto \Omega t$, $x\mapsto {\left(\hslash ∕m\Omega \right)}^{1∕2}x$. The numerical solution uses a discrete space-time grid with time step $dt=0.1$, and $2^{14}$ space points spaced $dx=0.0294$ units.

Figure 2

(Color online) Normalized density profiles of the coherent (noise averaged) field for different expansion times. Symbols, Monte Carlo results; dashed lines, Gaussian approximate solution to Eq. (5), ${\mid {\psi }_{\mathrm{c}}(x,t)\mid }^2=\left[N∕\left(\sqrt{2\pi }u\right(t)\right]e^{-\gamma t}\exp \left[-x^2∕\left(2u^2\right(t)\right]$ with $u\left(t\right)$ solving Eq. (10). Inset: coherent fraction (relative particle number). Crosses (open circles): Monte Carlo results for $\gamma =1$ $\left(\gamma =0.1\right)$. Dashed (solid) line: exponential decay with decoherence rate $\gamma$ (renormalized rate ${\gamma }_{\text{eff}}=0.82\gamma$). Units and all other parameters as in Fig. 1.

Figure 3

(Color online) Spatially averaged coherence function [Eq. (4)] for different expansion times (values and symbol coding as in Fig. 2). Symbols, Monte Carlo results; solid lines, kinetic theory [Eq. (8)] with ${\Gamma }_{\mathrm{i}}(s,0)\equiv 0$, renormalized decoherence rate ${\gamma }_{\text{eff}}=0.82\gamma$ and noise correlation length $l_{\text{eff}}=1.25l_{\text{corr}}$. Other parameters as in Fig. 1.

Figure 4

(Color online) Renormalized decoherence rate ${\gamma }_{\text{eff}}$ [Eq. (12)] for increasing interaction strength. On the $x$ axis is plotted the ratio $l_{\text{corr}}∕{\xi }_0\propto \sqrt{g}$, where ${\xi }_0$ is the healing length at the trap center, ${\xi }_0=1∕\sqrt{4g{n}_{\mathrm{c}}\left(x=0\right)}$. Large dots, Monte Carlo data (see text); small lower (upper) dots, numerical integration of Eq. (12) for a Thomas-Fermi (Gaussian) density profile. Dashed lines, asymptotics for a Thomas-Fermi profile at weak and strong interactions [Eq. (14)]; thick solid line, interpolation (15). The decoherence rate is normalized to its value $\gamma$ in an ideal gas.